Time Transfer – Algorithms for the Galileo Programme · Time Transfer – Algorithms for the...

Time Transfer – Algorithms for the Galileo Programme

John Davis 3rd June 2009

Monday, 22 March 2010

2

WHY DO WE NEED A STABLE REFERENCE TIMESCALE FOR GALILEO?

• Galileo will be used for time and frequency dissemination, requires traceability to UTC

• Stable timescale required for synchronising clocks on satellites, and obtaining optimal performance from Galileo’s navigation services.

Monday, 22 March 2010

3

REQUIREMENTS OF GALILEO REFERENCE TIMESCALE, GST(MC)

• Physical realisation of a timescale plus back- up GST(MC).

• TAI – GST(MC) < 50 ns (2σ)• TAI – GST(MC) uncertainty < 26 ns (2σ)• TAI – GST(MC) Normalised frequency

uncertainty < 5.4E-14 (2σ) (τ

= 1day) • GST(MC) normalised frequency stability <

4.5E-15 (τ

= 1day)

Monday, 22 March 2010

4

COMPUTATION AND AVAILABILITY OF UTC

• Coordinated Universal Time computed once per month by BIPM

• Based on an ensemble of mainly active hydrogen masers and high performance caesium clocks

• National standards laboratories maintain UTC(k) physical realisations of UTC,

• UTC – UTC(k) offsets computed up to 50 days in arrears

Monday, 22 March 2010

5

WHY DO WE NEED TIMESCALE ALGORITHMS?

• GST(MC) stability and reliability requirements cannot be achieved using a single clock

• Requirement to steer GST(MC) timescale to UTC / TAI

• Need to obtain best estimate of timescale offsets e.g. TAI – GST(MC) using satellite time transfer methods

Monday, 22 March 2010

6

TIME AND FREQUENCY RESPONSIBILITY WITHIN THE GALILEO REFERENCE

TIMESCALE

• Precise Time Facility (PTF) provides a stable physical timescale for navigation applications.

• Time Service Provider (TSP) provides the traceablilty to UTC / TAI, via several European UTC(k) laboratories.

Monday, 22 March 2010

7

CLOCK AND TIME TRANSFER NOISE MODELS

• Clock noise is modelled using a linear combination of Integrated Markov Noise Processes

• Close to FFM in the case of Active Hydrogen Masers • Close to WFM in the case of Caesium clocks

• Time transfer noise is modelled as linear combination of Markov Noise Processes

• Part way in characteristics between WPM and FPM, stationary in long term

• Similar model for TWSTFT, GPSCV and internal Galileo measurements

Monday, 22 March 2010

8

NOISE MODELS FOR CAESIUM CLOCKS AND ACTIVE HYDROGEN MASERS

Monday, 22 March 2010

9

NOISE MODELS FOR TWSTFT AND GPS CV MEASUREMENT NOISE

5 5.0005 5.001 5.0015 5.002

x 104

-1

0

1

2

3

4

5

6

7

8

9x 10

-9 Tim e Tra ns fe r Nois e S im ula tion

MJ D

Tim

e O

ffset

GP S CV TWS TFT

Monday, 22 March 2010

10

TWSTFT MODEL, ADEV, MDEV, HDEV CHARACTERISTICS

1 0 2

1 0 3

1 04

1 0 5

1 0 6

1 0 7

1 0 - 1 7

1 0 - 1 6

1 0 - 1 5

1 0 - 1 4

1 0 - 1 3

1 0 - 1 2 A D E V , H D E V M D E V T W S T F T

ta u

AD

EV /

MD

EV /

HD

EV

A D E V s im u la t io nH D E V s im u la t io nM D E V s im u la t io nA D E V e x p e c ta t io nH D E V e x p e c ta t io n M D E V e x p e c ta t io n

Monday, 22 March 2010

11

GPS CV MODEL, ADEV, MDEV, HDEV CHARACTERISTICS

1 0 2

1 03

1 04

1 0 5

1 06

1 071 0

- 1 6

1 0- 1 5

1 0- 1 4

1 0- 1 3

1 0- 1 2 A D E V , H D E V M D E V G P S C V

ta u

AD

EV /

MD

EV /

HD

EV

A D E V s im u la t io nH D E V s im u la t io nM D E V s im u la t io nA D E V e x p e c ta t io nH D E V e x p e c t a t io nM D E V e x p e c t a t io n

Monday, 22 March 2010

12

ENSEMBLE ALGORITHMS

• Aim is to produce a “composite” free running timescale from an ensemble of individual clocks

• Realised via estimates of (CClk – CI )• Early algorithms based on weighted mean

approach• Later algorithms based on use of Kalman

Filter, these are used in Galileo

Monday, 22 March 2010

13

ENSEMBLE ALGORITHM• TSP ensemble algorithm will include clocks from

several UTC(k) laboratories.

• Time Offset, Normalised Frequency Offset, Linear Frequency Drift and Integrated Markov Process state vector components for each clock

• Active hydrogen masers assumed to possess linear frequency drift, caesium clocks assumed to be free of linear frequency drift

Monday, 22 March 2010

14

ENSEMBLE ALGORITHM

• Long term, ensemble timescale will be free of linear frequency drift

• Close to optimal stability at all averaging times

• Includes linear frequency drift in clock models

• May include white measurement noise

Monday, 22 March 2010

15

COMBINING CLOCKS WITH DIFFERENT STABILITY CHARACTERISTICS

2 2 . 5 3 3 . 5 4 4 . 5 5 -1 5 . 8

-1 5 . 6

-1 5 . 4

-1 5 . 2

-1 5

-1 4 . 8

-1 4 . 6

-1 4 . 4

-1 4 . 2

L o g 1 0 ( τ )

Log 10

(σy)

C lo c k 1 (F F M ) C lo c k 2 (W F M ) C lo c k 3 (W F M ) C o m p o s ite S im p le C o m p o s ite O p t im a l C o m p o s ite

Monday, 22 March 2010

16

ENSEMBLE ALGORITHM PERFORMANCE, 2 HYDROGEN MASERS + 4 CAESIUM CLOCKS

Monday, 22 March 2010

17

WHITENESS OF RESIDUALS

5.0008 5.0008 5.0009 5.0009 5.001

x 104

-6

-4

-2

0

2

4

6 x 10

-12 Clock 2 - Clock1, Res idua ls ,

MJD

Res

idua

ls

Monday, 22 March 2010

18

REMAINING ISSUES

• Treatment of non-white measurement noise

• Difference in noise levels between and within laboratories.

• Biases in time transfer measurements

Monday, 22 March 2010

19

TIME TRANSFER COMBINING ALGORITHMS

• Use range of satellite time transfer measurements to estimate offset between two distant timescales

• UTC(j) – UTC(k) links

• Offset between two separate PTF reference timescales

• GST(MC) – GPS_Time offset

Monday, 22 March 2010

20

ALGORITHM PROPERTIES

• Kalman filter based• Multiple input data sets in single algorithm:

TWSTFT, GPSCV, internal Galileo products • Use of both TWSTFT and GPSCV calibration

within algorithm• Model calibration offset as long relaxation time

Markov Process • Timescale and time transfer models already

described

Monday, 22 March 2010

21

ALGORITHM PERFORMANCE

• Separately weight short term noise and calibration uncertainties of TWSTFT and GPSCV data

• Maintain TWSTFT calibration uncertainty on loss of TWSTFT data

• Good performance in case of missing data

Monday, 22 March 2010

22

ESTIMATION PERFORMANCE OF TIME TRANSFER COMBINING ALGORITHM

5 5 .0 0 0 5 5 .0 0 1 5 .0 0 1 5 5 .0 0 2

x 1 04

-0 .5

0

0 .5

1 .0

1 .5

2 x 1 0

-9 T im e O ffs e t E s tim a tio n E rro r

M J D

Tim

e O

ffset

T im e O ffs e t E rro r T im e O ffs e t E rro r E xp e c ta tio n

Monday, 22 March 2010

23

STEERING AND PREDICTION ALGORITHMS

• Based on time transfer combining algorithms

• Kalman filter based timescale predictor added to deal with delays in data set availability

• Steering algorithm added, to either minimise time offset or frequency offset

Monday, 22 March 2010

24

PERFORMANCE OF A STEERING ALGORITHM

Monday, 22 March 2010

25

FIRST RESULTS FROM TSP

Steered and unsteered timescales

-8.00E-08

-6.00E-08

-4.00E-08

-2.00E-08

0.00E+00

2.00E-08

54400 54500 54600 54700 54800 54900

MJD

Tim

e O

ffset

steered unsteered

Monday, 22 March 2010

26

CONCLUSIONS

• NPL has developed a range of state of the art timescale algorithms

• Currently being developed for use in Galileo reference timescale.

• First TSP results within specification achieved